Department of Mathematics and Statistics, University of Prince Edward Island, 550, University Ave., Charlottetown, PE, C1E 4P3, Canada. E-mail: sislam@upei.ca
1This research is supported by the University of Prince Edward Island major research grant (MRG), Charlottetown, PE, Canada.
A position dependent random map is a discrete-time dynamical system consisting of a number of transformations such that the probability of selecting a transformation is a function of position. In this paper we describe a method of approximating piecewise linear invariant densities of absolutely continuous measures for position dependent random maps where the component maps satisfies average expanding condition. We prove the convergence of our method and present a numerical example.
Position dependent random maps, Frobenius-Perron operator, Absolutely continuous invariant measures, Piecewise linear approximation
